On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences

TL;DR

This paper explores the geometric structure of Nash and correlated equilibria under cumulative prospect theoretic preferences, revealing that CPT correlated equilibria can be disconnected and differ from classical convex polytopes.

Contribution

It characterizes the geometry of CPT equilibria, showing they can be disconnected and differ from classical convex sets, and provides explicit characterizations for 2x2 games.

Findings

CPT correlated equilibria may be disconnected sets.

All CPT Nash equilibria lie on the boundary of CPT correlated equilibria.

Explicit characterizations for 2x2 games are provided.

Abstract

It is known that the set of all correlated equilibria of an n-player non-cooperative game is a convex polytope and includes all the Nash equilibria. Further, the Nash equilibria all lie on the boundary of this polytope. We study the geometry of both these equilibrium notions when the players have cumulative prospect theoretic (CPT) preferences. The set of CPT correlated equilibria includes all the CPT Nash equilibria but it need not be a convex polytope. We show that it can, in fact, be disconnected. However, all the CPT Nash equilibria continue to lie on its boundary. We also characterize the sets of CPT correlated equilibria and CPT Nash equilibria for all 2x2 games.